What is Long Run Average Cost (LRAC) and Long Run Marginal Cost (LRMC)?
Introduction
The costs of a firm are discussed in the context of time periods. There are two segregations in time periods under which the firm operates i.e., Short Run and Long Run. Short Run for a firm is a time period in which at least one or few factors of production or inputs are fixed or constant i.e., they cannot be varied to achieve desired production or output level. Such factors of production are known as Fixed Factors. Rest of the factors of production can be varied and such factors are known as Variable Factors. On the other hand, Long Run for a firm is a time period in which firm can vary all the factors of production or inputs in order to achieve desired level of production or output. The costs incurred by firm in the short run are called Short Run Costs and costs incurred by firm in the long run are called Long Run Costs.
In previous sessions, we discussed Short Run Costs and shapes of their curves in detail in a 3-part series. Under short run cost curves, we discussed Total Fixed Cost (TFC), Total Variable Cost (TVC), Total Cost (TC), Average Fixed Cost (AFC), Average Variable Cost (AVC), Short Run Marginal Cost (SMC) and Short Run Average Cost (SAC).
In this session we are going to discuss in detail the Long Run Costs and shapes of the Long Run Cost Curves.
Long Run Costs
As explained earlier, Long Run is a time period for a firm, in which firm can vary all factors of production i.e., all inputs are variable for the firm. And as there are no fixed factors of production, so there are no fixed costs for a firm in the long run. Therefore, the Total Variable Cost (TVC) and Total Cost (TC) becomes the same and coincide in the long run as every cost is variable.
Long Run Average Cost (LRAC)
The Long Run Average Cost is the cost per unit of output. The Long Run Average Cost can be derived as
LRAC = Total Cost/ Output i.e., LRAC = TC/ q
Long Run Marginal Cost (LRMC)
The Long Run Marginal Cost is the change in Total Cost per unit of change in output. If the production changes from (n-1) units to n units, the marginal cost of producing the nth unit of output can be derived as
LRMC = Total Cost at n units – Total Cost at (n-1) units
In the long run too, similarly like short run, the sum of all the marginal costs up to n level of output gives the total cost for the n level of output.
Shape of Long Run Cost Curves
It becomes important to understand the trend of Long Run Average Cost (LRAC) Curve and Long Run Marginal Cost (LRMC) Curve in the context of change in the input proportions and the level of output.
Before moving on to shape of curve, we need to discuss what is the factor or force behind the shaping the long run cost curves which is nothing but different Return to Scales.
Returns to Scales shaping the Long Run Cost Curves
In the long run all factors of production becomes variable and hence firms vary all the inputs simultaneously in order to achieve the desired level of output in the long run. Here for simplicity to understand, let us say that firm varies all the inputs simultaneously in the same proportion in order to bring a change in the level of output. Now this change in the input proportion can lead to different changes in output.
Depending on what change takes place in the output, the Returns to Scales can be divided into three categories as follows.
Case 1) Increasing Returns to Scale (IRS) and its impact on Long Run Average Cost (LRAC)
When all inputs are increased or scaled by a certain proportion and if that results (returns) into increase in output by larger proportion than that of input, that phenomenon is known as Increasing Returns to Scale (IRS). In other words, to increase output by a certain proportion, the input needs to be increased by lesser proportion then that of output. Thus at given input prices, the additional cost incurred to increase inputs would be of lesser proportion than the proportional increase in output resulted from the same.
In simple terms, if a firm wants to double the output, in case of increasing return to scale, the firm will need to increase the inputs but less than the double of earlier levels. So smaller increase in inputs leading to bigger increase in output.
So what happens to the Long Run Average Cost of a firm when the firm is getting Increasing return to scale in its production process. So when firm operates with increasing returns to scale, the long run average cost for the firm falls as the firm increases the output.
Case 2) Decreasing Returns to Scale (DRS) and its impact on Long Run Average Cost (LRAC)
When all inputs are increased or scaled by a certain proportion and if that results (returns) into increase in output by lesser proportion than that of input, that phenomenon is known as Decreasing Returns to Scale (DRS). In other words, to increase output by a certain proportion, the input needs to be increased by larger proportion then that of output. Thus at given input prices, the additional cost incurred to increase inputs would be of larger proportion than the proportional increase in output resulted from the same.
So to say, when firm operates with decreasing returns to scale, the long run average cost for the firm rises as the firm increases the output.
Case 3) Constant Returns to Scale (CRS) and its impact on Long Run Average Cost (LRAC)
When all inputs are increased or scaled by a certain proportion and if that results (returns) into increase in output by equal proportion as that of input, that phenomenon is known as Constant Returns to Scale (CRS). In other words, to increase output by a certain proportion, the input needs to be increased by same or equal proportion as that of output. Thus at given input prices, the additional cost incurred to increase inputs would be of equal proportion with the proportional increase in output resulted from the same.
So to say, when firm operates with constant returns to scale, the long run average cost for the firm remains constant as the firm increases the output.
Shape of Long Run Average Cost (LRAC) Curve and Long Run Marginal Cost (LRMC) Curve
For a typical firm, increasing returns to scale is observed at initial stages of production which is followed by constant returns to scale and finally followed by decreasing returns to scale. Thus as discussed above the impact of returns to scale on the LRAC would be same i.e., the LRAC curve will fall initially during IRS, will remain constant during CRS and finally LRAC curve will rise during DRS. Hence the LRAC curve is U – Shaped.
The above graph shows the Long Run Average Cost (LRAC) curve and Long Run Marginal Cost (LRMC) curve. The horizontal axis shows the output and the vertical axis shows the costs. For the 1st unit of output, as AC and MC are same, the LRAC and LRMC are the same. And as explained above, as the output increases initially, the LRAC falls. And that is followed by a point where the LRAC remains constant and finally after that point, with increasing output, the LRAC rises.
Now we know, that as far as the LRAC is falling, the LRMC must be less than the LRAC and when the LRAC is rising, the LRMC must be greater than the LRAC. Hence even the LRMC curve is U – Shaped.
In the above graph, it can be seen that the LRMC curve cuts the LRAC curve from below at minimum point of LRAC i.e., A with corresponding output of q. To the left of q, the LRAC is falling and LRMC is lesser than the LRAC and to the right of q, the LRAC is rising and LRMC is higher than the LRAC.
Conclusion
In this session, we discussed in detail about the Long Run Costs and the Shapes of the Long Run Cost Curves namely, Long Run Average Cost (LRAC) and Long Run Marginal Cost (LRMC).
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